# Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions

@inproceedings{Balmaseda2021QuantumCO, title={Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions}, author={Aitor Balmaseda and Davide Lonigro and Juan Manuel P'erez-Pardo}, year={2021} }

. We investigate the controllability of an inﬁnite-dimensional quantum system: a quantum particle conﬁned on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with quasi- δ boundary conditions. This is a particular class of self-adjoint boundary conditions compatible with the graph structure. We prove that global approximate controllability can be achieved using two physically distinct protocols: either using the boundary…

## References

SHOWING 1-10 OF 90 REFERENCES

### A General Approximation of Quantum Graph Vertex Couplings by Scaled Schrödinger Operators on Thin Branched Manifolds

- MathematicsCommunications in Mathematical Physics
- 2013

We demonstrate that any self-adjoint coupling in a quantum graph vertex can be approximated by a family of magnetic Schrödinger operators on a tubular network built over the graph. If such a manifold…

### Quantum graphs: I. Some basic structures

- Mathematics
- 2004

A quantum graph is a graph equipped with a self-adjoint differential or pseudo-differential Hamiltonian. Such graphs have been studied recently in relation to some problems of mathematics, physics…

### Boundary dynamics and topology change in quantum mechanics

- Mathematics, Physics
- 2015

We show how to use boundary conditions to drive the evolution on a Quantum Mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schr\"{o}dinger equation. In…

### GLOBAL THEORY OF QUANTUM BOUNDARY CONDITIONS AND TOPOLOGY CHANGE

- Mathematics
- 2004

We analyze the global theory of boundary conditions for a constrained quantum system with classical configuration space a compact Riemannian manifold M with regular boundary Γ=∂M. The space ℳ of…

### Convergence of resonances on thin branched quantum waveguides

- Mathematics
- 2007

We prove an abstract criterion stating resolvent convergence in the case of operators acting in different Hilbert spaces. This result is then applied to the case of Laplacians on a family Xe of…

### On the controllability of bilinear quantum systems

- Mathematics
- 2000

We present in this paper controllability results for quantum systems interacting with lasers. A negative result for infinite dimensional spaces serves as a starting point for a finite dimensional…

### Quantum Wires with Magnetic Fluxes

- Mathematics
- 2003

Abstract: In the present article magnetic Laplacians on a graph are analyzed. We provide a complete description of the set of all operators which can be obtained from a given self-adjoint Laplacian…

### Controllability of the discrete-spectrum Schrödinger equation driven by an external field

- Mathematics
- 2009

### On global approximate controllability of a quantum particle in a box by moving walls

- Mathematics
- 2022

We study a system composed of a free quantum particle trapped in a box whose walls can change their position. We prove the global approximate controllability of the system. That is, any initial state…